Ontario, Canada · Curriculum spine
Grade 9
67 concepts across 1 subject. Codes follow the ministry's own expectation numbers; where a course is broken into bites (chapter.bite), each bite names the expectations it covers.
Mathematics (MTH1W)
The Ontario Curriculum, Grade 9: Mathematics, 2021 (de-streamed) · 67 concepts
Strand A1
Social-Emotional Learning Skills and the Mathematical Processes
Persevering, managing stress, working with others, and using the mathematical processes.
- A1.1Coming soonThinking like a mathematicianUse the mathematical processes: problem solving, reasoning, reflecting, connecting, communicating, and keep going when it is hard.
Chapter 110
Chapter 1 · Numbers & Sets
Unit 1 at school (11 days). What kinds of numbers there are, how they behave, and the rules that never break.
- 1.1Free to tryCounting numbers, then zero, then the negatives: natural, whole and integer, and how the sets sit inside each other.
- 1.2Lesson readyFractions and decimals that end or repeat are rational; √2 and π are not. Plus the 5 000-year story of how we got our digits.
- 1.3Lesson readyA sign says which side of zero. Add, subtract, multiply and divide signed numbers and know why the rules hold.
- 1.4Lesson readyWrite the powers out and the exponent laws appear. Then walk the decimal point to write huge and tiny numbers.
- 1.5Lesson readyFind the target digit, look at the one after it, and let the rest go. Decimal places and significant figures.
- 1.6Lesson readyBEDMAS: brackets, exponents, then divide and multiply left to right, then add and subtract left to right.
- 1.7Lesson readyA fraction is a count of one kind of piece. Compare with common pieces; add and subtract with common denominators; flip to divide.
- 1.8Lesson readyInfinitely many is not a big number, it is a list that never ends. A limit is what a sequence gets closer and closer to.
- 1.9Lesson readyBetween any two rational numbers there is always another one. Integers do not do that.
- 1.10Lesson readyPercent is a fraction of 100; a rate is an amount for one. Not on the school's Unit 1 handout, here so nothing on the Ministry list is missed.
Chapter 212
Chapter 2 · Ratios & Exponents
Substitution, ratios and proportions, rates and percent, then every exponent law, from the very beginning. Ends with a full exam review.
- 2.1Free to tryPut each number in brackets in place of its letter, then BEDMAS. Tables of values and the distributive property.
- 2.2Lesson readyPart-to-part and part-to-whole, two- and three-term ratios, equivalent ratios, and lowest terms by the GCF.
- 2.3Lesson readyTwo equal ratios: find the missing term with the proportionality constant or by cross-multiplying; three-term proportions.
- 2.4Lesson readyAdd the parts, find one block, build each share; problems where one part is known instead of the total.
- 2.5Lesson readyRates compare different units; unit rates, best buys, conversions, exchange rates and map scales.
- 2.6Lesson readyFractions, decimals and percents; percent of a number, what percent, and finding the whole.
- 2.7Lesson readyDiscount, HST, tips, commission, markup, original price and repeated percents.
- 2.8Lesson readyBase and exponent, (−a)ⁿ versus −aⁿ, fractions to a power, and writing numbers as powers.
- 2.9Lesson readySame base: add exponents to multiply, subtract to divide; coefficients; the zero exponent.
- 2.10Lesson readyPower of a power, power of a product and power of a quotient, with coefficients and signs.
- 2.11Lesson readya⁻ⁿ = 1/aⁿ: flip across the fraction bar; mixing every law and writing answers with positive exponents.
- 2.12Lesson readyEvery question type from the unit, mixed, with the exam checklist.
Chapter 313
Chapter 3 · Polynomials
The words of algebra, naming and degree, like terms with algebra tiles, adding and subtracting, multiplying and dividing by a monomial, word problems and applications. Ends with an EQAO-style review.
- 3.1Free to tryVariable, coefficient, constant and term; expression versus equation.
- 3.2Lesson readyMonomial, binomial, trinomial by number of terms; writing in descending order.
- 3.3Lesson readyDegree of a term (add the exponents) and of a polynomial (the highest term).
- 3.4Lesson readySame variables and exponents = same tile shape; zero pairs; combining with tiles.
- 3.5Lesson readyGroup, add coefficients, clear double signs, simplify then evaluate; several variables.
- 3.6Lesson readyDrop the brackets and collect; the vertical method with placeholders; perimeter.
- 3.7Lesson readyFlip EVERY sign in the second bracket, then add; several variables; find the error.
- 3.8Lesson readyPerimeter of triangles, rectangles and trapezoids; races, costs and salary with commission.
- 3.9Lesson readyMonomial × monomial with the product law; the distributive property with tiles and area models.
- 3.10Lesson readyExpand every bracket then collect; negatives in front of brackets; nested brackets inside out.
- 3.11Lesson readyDivide every term; exponents subtract; check by multiplying back.
- 3.12Lesson readyArea, perimeter, shaded regions, boxes and volume; solving for x from a known perimeter.
- 3.13Lesson readyEvery question type in the unit, mixed, half of them EQAO-style.
Strand C15
Algebra
Expressions, equations, coding, and linear relations.
- C1.1Coming soonWhere an algebra idea came fromResearch the history of an algebraic concept, like the equals sign or variables.
- C1.2Coming soonWriting expressions for patternsCreate algebraic expressions that generalize a relationship shown in words, tables or diagrams.
- C1.3Coming soonAre these expressions equal?Compare expressions using properties of operations, substitution and models.
- C1.4Coming soonSimplifying expressionsCollect like terms and apply the distributive property to simplify expressions.
- C1.5Coming soonCreating and solving equationsWrite an equation for a situation, solve it, and check the solution.
- C2.1Coming soonCoding an algebra ideaWrite code that shows an algebraic concept, like evaluating an expression for many inputs.
- C2.2Coming soonDecomposing a problem into codeBreak a situation into computational steps and write code that runs them.
- C2.3Coming soonReading and changing codePredict what code will output and alter it to meet new constraints.
- C3.1Coming soonLinear or not?Compare graphs, tables and equations of linear and non-linear relations and explain how to tell them apart.
- C3.2Coming soonRepresenting linear relationsShow a linear relation with a table, a graph and an equation, and move between them.
- C3.3Coming soonWhere two lines meetCompare two linear relations and interpret their point of intersection in context.
- C4.1Coming soonRate of changeInterpret slope as a constant rate of change in a linear relation, and initial value as the intercept.
- C4.2Coming soonGraphing from an equationGraph lines given as x = k, y = k, ax + by = k and y = mx + b.
- C4.3Coming soonTransforming linesTranslate, reflect and rotate a line and describe how its equation changes.
- C4.4Coming soonEquation from a graph or tableFind the equation of a line from two points, a graph or a table.
Strand D6
Data
One- and two-variable data, scatter plots, and mathematical modelling.
- D1.1Coming soonBig data and its implicationsDescribe a current situation that involves a large amount of data and its potential impacts.
- D1.2Coming soonOne-variable dataRepresent and analyse one-variable data with appropriate graphs and summary measures.
- D1.3Coming soonScatter plots and lines of best fitCreate a scatter plot for two variables, describe the trend and draw a line of best fit.
- D1.4Coming soonPredicting and correlationUse a line of best fit to make predictions and describe the strength of a correlation.
- D2.1Coming soonWhy model mathematicallyDescribe the value of mathematical modelling and how it is used to make decisions.
- D2.2Coming soonModelling a real situationApply the modelling process to a real-life situation and communicate the results.
Strand E6
Geometry and Measurement
Geometric relationships, units, dimensions, and composite measures.
- E1.1Coming soonWhere a geometry idea came fromResearch the history of a geometric concept, like pi or the Pythagorean theorem.
- E1.2Coming soonDesigns with geometric relationshipsCreate and analyse designs using angles, symmetry and shapes.
- E1.3Coming soonConverting unitsSolve problems converting within and between measurement systems.
- E1.4Coming soonChanging dimensionsShow how changing a dimension changes perimeter, area, surface area and volume.
- E1.5Coming soonComposite shapes and solidsSolve problems involving perimeter, area, surface area and volume of composite figures.
- E1.6Coming soonPythagoras and similar trianglesUse the Pythagorean theorem and similar triangles to find unknown lengths.
Strand F4
Financial Literacy
Financial decisions, appreciation and depreciation, credit, budgets.
- F1.1Coming soonLearning from a financial situationAnalyse a past or current financial situation and what it teaches about decisions.
- F1.2Coming soonAppreciation and depreciationIdentify things that gain or lose value over time and model the change.
- F1.3Coming soonComparing creditCompare interest rates, fees and rewards on credit options and explain the trade-offs.
- F1.4Coming soonAdjusting a budgetModify a budget to reflect a change in circumstances and justify the changes.